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š¬ Same speed, still accelerating?
On a merry-go-round the speed can stay constant, yet the motion is accelerated. How can that be?
What is uniform circular motion, and its distance and displacement?
Uniform Circular Motion
Uniform
the speed stays constant — it never changes value
Circular motion
the object moves along a circular path
↓
Uniform circular motion = motion along a circular path at a constant speed.
One complete revolution of a circle of radius R
Distance travelled
2π R
— the whole circumference
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Displacement
zero — the object comes back to where it started
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Average speed
v
av
=
2π R
T
(4.5), the same at every point on the circle
↓
Average velocity over one revolution = 0, but the average speed is not zero.
- When an object moves in a circular path, its motion is circular motion . If the speed is constant, it is uniform circular motion .
- In one revolution of a circle of radius R : distance travelled = 2π R (the circumference), but displacement = 0 (it returns to the start).
- If one revolution takes time T : v av = 2π R T (4.5) while the average velocity over one revolution is 0.
ā Note
- We calculated the average speed (Eq. 4.5) for one revolution but for uniform circular motion since the speed is constant, its value is the same at every point on the circle.
Why is uniform circular motion accelerated?
Why constant speed can still mean acceleration
Velocity changes if…
its magnitude changes, OR its direction changes, or both
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In uniform circular motion
the speed is constant, but the direction of the velocity changes at every point
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So the velocity is changing
and the velocity is along the tangent to the circle at each point
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A changing velocity means acceleration — uniform circular motion is an accelerated motion.
- Velocity changes if its magnitude or its direction (or both) changes.
- In uniform circular motion the speed is constant, but the direction of velocity changes continuously — so the motion is accelerated .
- The velocity at any point is along the tangent to the circle at that point, in the direction of motion.
Important Definitions
- Circular motion — the motion of an object moving along a circular path.
- Uniform circular motion — motion of an object in a circular path with constant (uniform) speed; it is accelerated because the direction of velocity keeps changing.
- Tangent — a straight line that meets the circle at one and only one point; the velocity at a point is along the tangent at that point, in the direction of motion.
š¹ Ready to Go Beyond — tangent to a circle
- The velocity at a point is along the tangent to the circle at that point, in the direction of motion.
- A tangent is a straight line that meets the circle at one and only one point. You will learn more about it in Mathematics.
In this Activity, we will spin a marble inside a ring and then lift the ring to discover the direction in which the freed marble moves.
Steps
- Place a ring (e.g. an adhesive-tape ring) flat on a smooth surface and roll a marble so it goes around the inner boundary.
- After a revolution or two, lift the ring without disturbing the marble. What path does the marble now take?
- Repeat a few times to confirm.
What you observe
- Once released, the marble moves in a straight line — along the direction (tangent) it had at the instant the ring was removed. You will learn the reason in a later chapter.
ā Note
- In uniform circular motion the speed is constant at every point; only the direction of velocity changes .
- Uniform circular motion is an idealised model, yet a useful one — it underlies planets orbiting the Sun and a vehicle making a circular turn.
ā Note
- In everyday life we call a vehicle ‘accelerating’ only when its speed changes, but a change in the direction of velocity is acceleration too — something we often fail to recognise.
NCERT Question 3 — A girl is riding her
A girl is riding her scooter and finds that its speedometer reading is constant. Is it possible for her scooter to be accelerating and if so, how?
NCERT Question 16 — Rohan studies science from 6
Rohan studies science from 6 PM to 7:30 PM at home. Consider the tip of the minute’s hand of the wall clock. During the given time interval, what is its: (i) distance travelled, (ii) displacement, (iii) speed, and (iv) velocity. The length of the minute’s hand is 7 cm (Fig. 4.32).
š¹ Ready to Go Beyond — motion in three dimensions
- Motion in space — a car climbing up a mountain road, a bird flying in the sky, or an aircraft moving through air — is called motion in three dimensions . You will learn about it in higher grades.
Concept Map
Motion
A change of position with time, judged from a reference point.
Straight-line motion
Position, distance and displacement along a line.
Speed, velocity, acceleration
Averages and rates of change of position and velocity.
Kinematic equations
v=u+at, s=ut+½at², v²=u²+2as (constant a).
Motion graphs
A visual picture of how motion changes with time.
Position-time & velocity-time
Slope and area give velocity, acceleration and displacement.
Motion in a plane
Two-dimensional motion such as circular paths.
Uniform circular motion
Constant speed but continuously changing direction, so accelerated.
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Test Yourself
-
In one full revolution of a circle of radius R, what are the distance travelled and the displacement?
Show Answer
Distance travelled = 2πR (the circumference); displacement = 0, because the object returns to its starting point. -
Why is uniform circular motion an accelerated motion even though the speed is constant?
Show Answer
Because the direction of the velocity changes continuously, so the velocity changes — and a changing velocity means acceleration. -
In which direction is the velocity at any point on a circular path?
Show Answer
Along the tangent to the circle at that point, in the direction of motion. -
What is the average velocity of an object over one complete revolution?
Show Answer
Zero, since the displacement over one full revolution is zero.
